Related papers: Massey Products and Ideal Class Groups

The power classes of a field are well-known for their ability to parameterize elementary $p$-abelian Galois extensions. These classical objects have recently been reexamined through the lens of their Galois module structure. Module…

Let $p$ be an odd prime and $L/K$ a $p$-adic Lie extension whose Galois group is of the form $\mathbb{Z}_p^{d-1}\rtimes \mathbb{Z}_p$. Under certain assumptions on the ramification of $p$ and the structure of an Iwasawa module associated to…

We show that any triple Massey product with respect to prime 2 contains 0 whenever it is defined over any field. This extends the theorem of M. J. Hopkins and K. G. Wickelgren, from global fields to any fields. This is the first time when…

We construct two families of examples of pro-p groups, with rather elementary presentations, that do not complete into 1-cyclotomic oriented pro-p groups. These provide brand new examples of pro-p groups that do not occur as maximal pro-p…

For a number field $K$, we consider $K^{\rm ta}$ the maximal tamely ramified algebraic extension of~$K$, and its Galois group $G^{\rm ta}_K= Gal(K^{ta}/K)$. Choose a prime $p$ such that $\mu_p \not \subset K$. Our guiding aim is to…

Let $p$ be an odd prime and $F_{\infty}$ a $p$-adic Lie extension of a number field $F$ with Galois group $G$. Suppose that $G$ is a compact pro-$p$ $p$-adic Lie group with no torsion and that it contains a closed normal subgroup $H$ such…

For a number field K and a prime number p we denote by BP\_K the compositum of the cyclic p-extensions of K embeddable in a cyclic p-extension of arbitrary large degree. Then BP\_K is p-ramified (= unramified outside p) and is a finite…

For a number field $k$ and an odd prime number $p$, we consider the maximal multiple $\mathbb{Z}_p$-extension $\tilde{k}$ of $k$ and the unramified Iwasawa module $X(\tilde{k})$, which is the Galois group of the maximal unramified abelian…

In this paper, we develop a new necessary and sufficient condition for the vanishing of 4-Massey products of elements in the mod-2 Galois cohomology of a field. This new description allows us to define a splitting variety for 4-Massey…

We develop the foundations of effective ultraproducts of fields and their Galois groups using the methods of computability theory. These computability-theoretic analogs of ultraproducts are called cohesive products, since the role of an…

The classical deformation theory of Lie algebras involves different kinds of Massey products of cohomology classes. Even the condition of extendibility of an infinitesimal deformation to a formal one-parameter deformation of a Lie algebra…

Let $p$ be a prime number and let $F$ be a field of characteristic different from $p$. We prove that there exist a field extension $L/F$ and $a,b,c,d$ in $L^{\times}$ such that $(a,b)=(b,c)=(c,d)=0$ in $\mathrm{Br}(F)[p]$ but $\langle…

Let $p$ be a prime, let $K$ be a discretely valued extension of $\mathbb{Q}_p$, and let $A_{K}$ be an abelian $K$-variety with semistable reduction. Extending work by Kim and Marshall from the case where $p>2$ and $K/\mathbb{Q}_p$ is…

We observe that some basic but fundamental constructions in Galois theory can be used to obtain some interesting restrictions on the structure of Galois groups of maximal $p$-extensions of fields containing a primitive $p$th root of unity.…

Let $\{\rho_\ell\}_\ell$ be the system of $\ell$-adic representations arising from the $i$th $\ell$-adic cohomology of a complete smooth variety $X$ defined over a number field $K$. Let $\Gamma_\ell$ and $\mathbf{G}_\ell$ be respectively…

- Let K be a totally imaginary number field. Denote by G ur K (2) the Galois group of the maximal unramified pro-2 extension of K. By comparing cup-products in {\'e}tale cohomology of SpecO K and cohomology of uniform pro-2 groups, we…

Let F be a Henselian valued field with char(F) = p and D a semi-ramified, "not strongly degenerate" p-algebra. We show that all Galois subfields of D are inertial. Using this as a tool we study generic abelian crossed product p-algebras,…

In this article we trace the genesis of a theorem that gives for the first time examples of Galois group $G_S$ of the maximal $p$-extension of $\mathbb{Q}$, unramified outside a finite set of primes not containing $p$, that are of…

We consider the p-Zassenhaus filtration (G_n) of a profinite group G. Suppose that G=S/N for a free profinite group S and a normal subgroup N of S contained in S_n. Under a cohomological assumption on the n-fold Massey products (which holds…

Let $p$ be an odd prime and $F$ be a number field whose $p$-class group is cyclic. Let $F_{\{\mathfrak{q}\}}$ be the maximal pro-$p$ extension of $F$ which is unramified outside a single non-$p$-adic prime ideal $\mathfrak{q}$ of $F$. In…